Complex coacervation: a field theoretic simulation study of polyelectrolyte complexation.

Using the complex Langevin sampling strategy, field theoretic simulations are performed to study the equilibrium phase behavior and structure of symmetric polycation-polyanion mixtures without salt in good solvents. Static structure factors for the segment density and charge density are calculated and used to study the role of fluctuations in the electrostatic and chemical potential fields beyond the random phase approximation. We specifically focus on the role of charge density and molecular weight on the structure and complexation behavior of polycation-polyanion solutions. A demixing phase transition to form a "complex coacervate" is observed in strongly charged systems, and the corresponding spinodal and binodal boundaries of the phase diagram are investigated.

Effects of sequence disorder on DNA looping and cyclization.

Effects of sequence disorder on looping and cyclization of the double-stranded DNA are studied theoretically. Both random intrinsic curvature and inhomogeneous bending rigidity are found to result in a remarkably wide distribution of cyclization probabilities. For short DNA segments, the range of the distribution reaches several orders of magnitude for even completely random sequences. The ensemble averaged values of the cyclization probability are also calculated, and the connection to the recent experiments is discussed.

Deposit growth in the wetting of an angular region with uniform evaporation.

Solvent loss due to evaporation in a drying drop can drive capillary flows and solute migration. The flow is controlled by the evaporation profile and the geometry of the drop. We predict the flow and solute migration near a sharp corner of the perimeter under the conditions of uniform evaporation. This extends the study of Popov and Witten [Phys. Rev. E 68, 036306 (2003)], which considered a singular evaporation profile, characteristic of a dry surrounding surface. We find the rate of the deposit growth along contact lines in early and intermediate time regimes. Compared to the dry-surface evaporation profile of Popov and Witten [Phys. Rev. E 68, 036306 (2003)], uniform evaporation yields more singular deposition in the early time regime, and nearly uniform deposition profile is obtained for a wide range of opening angles in the intermediate time regime. Uniform evaporation also shows a more pronounced contrast between acute opening angles and obtuse opening angles.

Effects of kinks on DNA elasticity.

We study the elastic response of a wormlike polymer chain with reversible kinklike structural defects. This is a generic model for (a) the double-stranded DNA with sharp bends induced by binding of certain proteins, and (b) effects of trans-gauche rotations in the backbone of the single-stranded DNA. The problem is solved both analytically and numerically by generalizing the well-known analogy to the quantum rotator. In the small stretching force regime, we find that the persistence length is renormalized due to the presence of the kinks. In the opposite regime, the response to the strong stretching is determined solely by the bare persistence length with exponential corrections due to the "ideal gas of kinks." This high-force behavior changes significantly in the limit of high bending rigidity of the chain. In that case, the leading corrections to the mechanical response are likely to be due to the formation of multikink structures, such as kink pairs.

Evaporative deposition patterns: spatial dimensions of the deposit.

A model accounting for the finite spatial dimensions of the deposit patterns in evaporating sessile drops of a colloidal solution on a plane substrate is proposed. The model is based on the assumption that the solute particles occupy finite volume and hence these dimensions are of steric origin. Within this model, the geometrical characteristics of the deposition patterns are found as functions of the initial concentration of the solute, the initial geometry of the drop, and the time elapsed from the beginning of the drying process. The model is solved analytically for small initial concentrations of the solute and numerically for arbitrary initial concentrations of the solute. The agreement between our theoretical results and the experimental data is demonstrated, and it is shown that the observed dependence of the deposit dimensions on the experimental parameters can indeed be attributed to the finite dimensions of the solute particles. These results are universal and do not depend on any free or fitting parameters; they are important for understanding evaporative deposition and may be useful for creating controlled deposition patterns.

Characteristic angles in the wetting of an angular region: deposit growth.

Solids dispersed in a drying drop migrate to the (pinned) contact line. This migration is caused by outward flows driven by the loss of the solvent due to evaporation and by geometrical constraint that the drop maintains an equilibrium surface shape with a fixed boundary. Here, in continuation of our earlier paper, we theoretically investigate the evaporation rate, the flow field, and the rate of growth of the deposit patterns in a drop over an angular sector on a plane substrate. Asymptotic power laws near the vertex (as distance to the vertex goes to zero) are obtained. A hydrodynamic model of fluid flow near the singularity of the vertex is developed and the velocity field is obtained. The rate of the deposit growth near the contact line is found in two time regimes. The deposited mass falls off as a weak power gamma of distance close to the vertex and as a stronger power beta of distance further from the vertex. The power gamma depends only slightly on the opening angle alpha and stays roughly between -1/3 and 0. The power beta varies from -1 to 0 as the opening angle increases from 0 degrees to 180 degrees. At a given distance from the vertex, the deposited mass grows faster and faster with time, with the greatest increase in the growth rate occurring at the early stages of the drying process.

Effects of flow on measurements of interactions in colloidal suspensions.

A hydrodynamic mechanism of interactions of colloidal particles is considered. The mechanism is based on the assumption of tiny background flows in the experimental cells during measurements by Grier et al. Both trivial (shear flow) and nontrivial (force propagation through viscous fluid) effects are taken into account for two colloidal particles near a wall bounding the solvent. Expressions for the radial (attractive or repulsive) forces and the polar torques are obtained. Quantitative estimates of the flow needed to produce the observed strength of attractive force are given; other necessary conditions are also considered. The following conclusion is made: the mechanism suggested most likely is not responsible for the attractive interactions observed in the experiments of Grier et al.; however, it may be applicable in other experimental realizations and should be kept in mind while conducting colloidal measurements of high sensitivity. Several distinctive features of the interactions due to this mechanism are identified.